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EFFICIENT PAPR REDUCTION TECHNIQUE BASED ON LOW COMPLEXITY MAX NORM ALGORITHM FOR OFDM SYSTEMS

1 M MADHUMITHA, 2 M PALANIVELAN

1 M.E. Communication Systems, 2Associate Professor, Dept. of ECE, Rajalakshmi Engineering College, Chennai, India

(e-mails: [email protected], [email protected])

ABSTRACT

Orthogonal Frequency Division Multiplexing (OFDM) is a proven technology in modern wireless communication because of its high data rate, ability to combat multipath fading and flexibility in digital signal processing. However, the peak to average power ratio (PAPR) of a transmitted signal is one of the main challenges in wideband multicarrier systems that use OFDM. High PAPR requires RF power amplifiers to be operated with large power back-offs which leads to inefficient amplification and expensive transmitters. The nonlinearities of the power amplifier cause out-of-band radiation and results in poor Bit Error Rate (BER) performance and loss in data rate. Therefore, it is desirable to reduce the PAPR in OFDM systems. In this paper, an efficient Low Complexity Max Norm (LCMN) algorithm to reduce the PAPR in OFDM system is proposed. This algorithm avoids the use of additional Inverse Fast Fourier Transform as compared to other conventional PAPR reduction schemes. Also, it provides better bandwidth utilization since it does not require transmission of side information to receiver. The performance measures Saving Gain, Amplifier Efficiency and BER of the proposed method has been evaluated and presented. The value of parametric constant introduced in the algorithm is optimised based on the performance measures considered.

Keywords OFDM, PAPR, LCMN, ILCMN, BER

1. INTRODUCTION

There is an ever increasing demand in the communication industry towards techniques that

could offer efficient bandwidth utilization, improved spectral efficiency, economical signal processing, high speed and low complexity hardware. Orthogonal Frequency Division Multiplexing has emerged to be one such promising technique in the recent years especially as the spectrum is becoming a more valuable resource. Subsequently, OFDM has become an appropriate choice for high bit rate communications and has been widely adopted in many wireless communication standards such as Wireless LAN (IEEE 802.11a), Digital Audio Broadcasting (DAB), Digital Video Broadcasting (DVB), and IEEE fixed broadband wireless access standard 802.16.

OFDM is a special type of multicarrier modulation [5, 6] in which a signal is split into several narrowband channels at different frequencies. The data is divided into parallel data streams each transmitted on a separate band [1, 2]. The transmission bandwidth, B in an OFDM system is divided into N orthogonal subcarriers, each having a bandwidth of f or B=N f . The orthogonality among the subcarriers results in the elimination of guard bands required by Frequency Division Multiplexing (FDM). The bandwidth is thus efficiently utilized in OFDM. Once the subcarriers are made orthogonal to each other, the interference among them is eliminated [3, 4]. Orthogonality means that the subcarriers are perpendicular to each other in a mathematical sense allowing the spectrum of each subcarrier to overlap another without interfering with it. Each subcarrier is modulated by Quadrature Amplitude Modulation (QAM) and the N data symbols are applied to the Inverse Fast Fourier Transform (IFFT) to obtain the time domain signal, ( )x t . The signal ( )x t which is transmitted via the transmitting PA and that has a period 1/T f can be expressed as in Equation (1).

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2

11

0

( ) ,k t

T

Nj

kNk

x t X e

0 ,t T (1)

where 10N

k kX

is the set of frequency domain symbols. Hence, OFDM as a transmission technique is known to have lot of strengths compared to any other transmission technique, such as its robustness to channel fading, its immunity to impulse interference, its high spectral efficiency and its ability in handling very strong echoes.

Despite lot many attractive features of OFDM, certain issues still remain in the design of OFDM systems. A major drawback of the OFDM signal is the high Peak to Average Power Ratio (PAPR) [4-7]. The transmit signal in OFDM exhibits a large PAPR which forces the Digital-to-Analog Converter (DAC) and the Power Amplifier (PA) to be operated with a high dynamic range. If this is not satisfied, the signal gets distorted severely and BER performance degradation occurs. A series of undesirable interference is encountered when the peak signal goes into the non-linear region of devices at the transmitter, such as intermodulation distortion and out-of-band radiation [4, 8]. One solution to this problem is to operate the power amplifier with large power backoffs but this leads to inefficient amplification and expensive transmitters. Therefore, it is highly desirable to reduce the PAPR of the OFDM signal before it drives the power amplifier.

The presence of a number of independently modulated subcarriers in an OFDM signal can give a large PAPR when added up coherently. When N signals are added with the same phase, they produce a peak power that is N times the average power. The PAPR of OFDM signals is defined as the ratio between the maximum instantaneous power and its average power. The PAPR of a continuous time signal, ( )x t is given by Equation (2):

2

2

max ( )

( )[ ( )] x t

E x tPAPR x t

(2)

For a discrete time signal, ( )x n expressed as,

2

11

0( )

knL N

Nj

kNk

x n X e

, n=0, 1, . . . , NL-1 (3)

where L is the oversampling factor, the PAPR is given by,

2

2

max ( )

( )[ ( )] x n

E x nPAPR x n

(4)

One of the most frequently employed performance measure for PAPR reduction is the Cumulative Distribution Function (CDF). However, instead of CDF, Complementary CDF (CCDF) is commonly used in most of the literature. CCDF is defined as the probability that the PAPR given by Equation (4) exceeds a threshold P0 and is expressed by Equation (5):

00( ) 1 (1 )P Np PAPR P e (5)

Several techniques to reduce the PAPR of OFDM system have appeared in the literature such as clipping, interleaving, coding schemes, constellation expansion, Selective Mapping (SLM), Partial



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Transmit Sequence (PTS), Tone Reservation (TR) and Tone Injection (TI). Each one of these techniques has its unique advantages and disadvantages.

In this paper, we propose a novel Low Complexity Max Norm (LCMN) algorithm to reduce the PAPR of OFDM signals. The key novelty of the algorithm is that it is linear, reversible and reduces PAPR at low computational complexity. This technique avoids the use of additional IFFT as compared to other conventional PAPR reduction schemes. Also, it provides better bandwidth utilisation since it does not require transmission of side information to the receiver. In addition, we present the analysis of Saving Gain, Amplifier Efficiency, and BER performance of the proposed technique.

2. RELATED WORK

A number of solutions to solve the high PAPR problem in OFDM systems have been addressed in the literature. These solutions can be largely classified as distortion or distortionless techniques. Distortion techniques like Amplitude Clipping, Filtering [9, 10, and 11], Coding [13, 14] create in-band distortion and peak regrowth. Coding schemes sacrifice the data rate. They require memory to store codewords and cause delay due to the time required to find a low PAPR codeword. Many distortionless techniques have also been proposed. The constellation expansion in [15] requires complex optimisation process, especially when the number of subcarriers is large. Simpler and practical constellation mapping techniques are active constellation extension [16] and tone reservation [17]. With selective mapping [18, 19], multiple sequences are generated from the original data block and the one with the lowest PAPR is selected for transmission. However, in order to recover the original data sequence, the side information must be transmitted to the receiver which decreases the information throughput. In the PTS approach [20], the disjoint subblocks of OFDM subcarriers are phase shifted separately after IFFT computation. The search for optimum subblock phase factors is computationally complex. Due to the usage of multiple IFFTs, PTS exhibits a high complexity proportional to the number of subblocks.

2.1 Nonlinear Characteristics of PA and DAC

The PA is employed in the transmitter to obtain sufficient transmit power. But the nonlinear characteristic of the PA is very sensitive to variations in signal amplitudes [8]. As a result, the signals entering into the nonlinear region introduce intermodulation between different subcarriers and cause out-of-band radiation. This leads to poor utilisation of bandwidth. Also, this additional interference leads to an increase in BER. Apart from this, if the PA is operated in a linear region with large power back-offs in order to keep the out of band power below the specified limits, it will lead to inefficient amplification and expensive transmitters. Therefore, it is important to aim at a power efficient operation of PA that provides adequate area coverage, saves power consumption, and allows small size terminals.

Large PAPR also demands the DAC to have a high dynamic range so as to accommodate the large peaks [3]. But this can be supported only by a high precision DAC, which although adds only reasonable amount of quantisation noise, it appears to be expensive. Alternatively, a low precision DAC would be cheaper but the quantisation noise will be significant and so it reduces the Signal to Noise Ratio (SNR).



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2.2 Power Amplifier Efficiency

We consider Class A power amplifier [12] in order to analyse both PAPR reduction and power efficiency. For Class A power amplifier, the overall efficiency is defined as,

outD C

PP (6)

where outP is the average output power of PA and DCP is the total DC power consumed by the PA.

We assume an ideal linear model for the PA, where linear amplification is achieved up to the saturation point [21]. Under these conditions, efficiency, is given by,

0.5

PAPR (7)

From Equation (7), it is seen that the PAPR is inversely proportional to the efficiency. Therefore, to obtain a high efficiency, it is important to apply a scheme that reduces the PAPR.

Solving Equations (6) and (7), we get a relation between the power consumption DCP and PAPR as:

2DC outP P PAPR (8)

Equation (8) signifies that if PAPR is reduced, then the consumed DC power DCP is also reduced. Hence, from Equation (8), we obtain an expression for power saving as

b asaving DC DC

P P P (9)

where bDC

P and aDC

P are DC power consumed by the PA before and after PAPR reduction respectively.

Substituting Equation (8) into Equation (9), we get,

2 ( )saving out b aP P PAPR PAPR (10)

where bPAPR and aPAPR are the PAPR obtained before and after reduction respectively.

Saving Gain is defined as /saving saving outG P P and is given by Equation (11) as:

2( )saving b aG PAPR PAPR (11)

3. PROPOSED SYSTEM

We propose a novel Low Complexity Max Norm (LCMN) algorithm to reduce the PAPR of OFDM signal. The proposed method overcomes the drawback of heavy computational complexity and phase search complexity found in conventional PAPR reduction techniques like SLM and PTS. It is



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also not required to transmit the side information, which is used to recover data at the receiver end. The block diagram of the proposed system is shown in Fig. 1.

Fig. 1: Proposed OFDM system with LCMN algorithm for PAPR reduction

The input data are mapped using 16-QAM modulation. Since QAM constellation is easy to implement, it is widely used. Then the QAM symbols are converted into parallel data streams and modulated using different subcarriers. All these signals are combined by the IFFT to change the frequency domain signals into time domain signals. To eliminate the effects of Intersymbol Interference (ISI), guard interval is introduced between the OFDM symbols. When individual signals with same phase are added up, it results in a large peak power. This peak power should be minimized before transmission of OFDM symbols in order to avoid signal distortion. In this section, a novel Low Complexity Max Norm algorithm has been proposed to reduce the PAPR.

3.1 LCMN Algorithm at Transmitter for PAPR Reduction The LCMN algorithm applied at the transmitter part to reduce PAPR includes the following steps.

Step 1: Generate the input data, d= (d1, d2, ..., di, ...., dN) and map the data with QAM constellation to get the modulated data stream, D.

Step 2: Calculate IFFT for the mapped data stream, D using d= IFFT (D).

Step 3: Find the maximum value from the values obtained in Step 2.

dmax = max (d1, d2, ....., di, ....., dN)

dmax = di

Step 4: Introduce a parameter, in order to define the parametric form of maximum norm. Multiply this parametric constant, with dmax.

*dmax = *[max (d1, d2, ....., di, ....., dN)]

*dmax = *di

where is a parameter that ranges from 0 to 1.

Step 5: Subtract the value of *di with each of the IFFT output to get a LCMN transformed data stream that promises a reduced PAPR.

x = d (*di)

x = ((d1 (*di)), (d2 (*di)), ..., (di (*di)), ..., (dN (*di))) (12)



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x = ((d1 (*di)), (d2 (*di)), ..., ((1 )*di), ..., (dN (*di)))

Step 6: Transmit the transformed output which offers low PAPR.

Inverse Low Complexity Max Norm (ILCMN) algorithm is applied at the receiver to recover the original signal. The transmitted signal is received by the receiving antenna and converted into parallel stream to apply it to Fast Fourier Transform (FFT). FFT changes the time domain signal into frequency domain signal to obtain the OFDM symbols from different subcarriers. Then the signal is demodulated to obtain the output binary symbols.

3.2 Inverse LCMN (ILCMN) Algorithm at the Receiver The Inverse LCMN (ILCMN) algorithm applied at the receiver part includes the following steps.

Step 1: Receive the transmitted data block, x

Step 2: Find the minimum value of x,

min (x) = min ((d1 (*di)), (d2 (*di)), ..., ((1 )*di), ..., (dN (*di))) (13)

min (x) = (1-)*di

Step 3: Divide min (x) by (1-) to obtain di.

min (x)/(1-) = di

Step 4: To obtain data block, d, add (*di) where di is the value obtained in Step 3 to the received data block, x. From Equation 12,

d = x + (*di)

d = ((d1 (*di) + (*di) ), (d2 (*di) + (*di)), ..., (di (*di) + (*di)), ..., (dN (*di) + (*di)))

d= (d1, d2, ..., di, ...., dN)

Step 5: Compute FFT for d obtained in Step 4, which yields the original data block.

4. RESULTS AND DISCUSSION

To evaluate the PAPR reduction performance of LCMN algorithm, simulations have been performed with MATLAB. In the simulation, we have used 16-QAM baseband modulation. Each modulated symbol is passed through N=64 subcarriers by 64 point IFFT. Table 1 lists the simulation parameters used.

Table 1: Simulation Parameters



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Fig. 2 shows the CCDF performance of LCMN with N=64 when varying parametric constant, . At the probability of clipping level 110-4, the original system offers 11.0dB, while the PAPR reduction technique incorporated in the proposed system reduces to 5.5 dB at the same level of clipping probability when =1. It is also observed that, if

Fig. 3 shows the Saving Gain for different values for N=64.

Fig. 3: Saving Gain Vs for N=64

Fig. 4 shows the BER performance of LCMN technique with different values.

Fig. 4: BER Performance of LCMN with =0.2, 0.4, 0.6 and 0.8

It is seen from Fig. 4 that, for values of >0.6, the BER performance is slightly degraded. Therefore, from Fig. 2, Fig. 3, Fig. 4, and Table 2, it is concluded that =0.6 achieves the required performance of the proposed system.

5. CONCLUSION

In this paper, a Low Complexity Max-Norm (LCMN) technique for PAPR reduction in OFDM system is proposed. To improve the PAPR reduction capability, a parametric constant is introduced in the proposed technique. It is seen from the simulation results that the proposed method offers a power reduction of 3.7 dB. In addition, Saving Gain, Amplifier Efficiency and BER performance of the proposed system were evaluated. The value of is optimized based on PAPR reduction, saving gain, efficiency and BER performance. The proposed scheme greatly reduces computational complexity since it uses only one IFFT. Also, it does not require side information to be transmitted to the receiver for recovery which avoids additional bandwidth and data rate loss.



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REFERENCES

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[3] Ramjee Prasad, OFDM for Wireless Communications Systems, Artech House Publishers, March 2004. [4] S. H. Han and J. H. Lee, An overview of peak-to-average power ratio reduction techniques for multicarrier transmission, IEEE Personal Communications, vol. 12, no. 2, pp. 56-65, April 2005. [5] Goldsmith A. Wireless communication. NewYork: Cambridge University Press; 2005. [6] T. S. Rappaport, Wireless Communications: Principles & Practice, 2nd edition, Prentice Hall Publishing 2001 [7] Van Nee, R., and Wild, A., Reducing the Peak to Average Power Ratio of OFDM, IEEE Vehicular Technology Conference, vol. 3, pp. 2072-2076, May1998. [8] Tao Jiang; Yiyan Wu, An Overview: Peak-to-Average Power Ratio Reduction Techniques for OFDM Signals, IEEE Transactions on Broadcasting, vol. 54, no.2, pp. 257 - 268, June 2008. [9] X. Li and L. J. Cimini, Effect of clipping and filtering on the performance of OFDMA, IEEE Commun. Lett., vol. 2, no. 5, pp. 131133, May 1998. [10] H. Ochiai and H. Imai, Performance analysis of deliberately clipped OFDM signals, IEEE Trans. Commun., vol. 50, no. 1, pp. 89101, Jan 2002. [11] Josef Urban and Roman Marsalek, OFDM PAPR Reduction by Combination of Interleaving with Clipping and Filtering, IEEE Communication Letter, pp. 249 252, June 2007. [12] Robert J. Baxley, G. Tong Zhou, Power Savings Analysis of Peak-to-Average Power Ratio Reduction in OFDM, IEEE Transactions on Consumer Electronics, vol. 50, no. 3, August 2004. [13] T. A. Wilkinson and A. E. Jones, Minimization of the peak to mean envelope power ratio in multicarrier transmission schemes by block coding, in Proc. IEEE Vehic. Tech. Conf., pp. 825831, July 1995. [14] V. Tarokh and H. Jafarkhani, On the computation and reduction of the peak-to-average power ratio in multicarrier communications, IEEE Trans. Commun., vol. 48, pp. 3744, January 2000. [15] J. Tellado, Peak to average power reduction for multicarrier modulation, Ph.D. thesis, Stanford University, 2000. [16] B. S. Krongold and D. L. Jones, PAR reduction in OFDM via active constellation extension, IEEE Trans. Broadcast., vol. 3, pp. 258268, Sept. 2003. [17] B. S. Krongold and D. L. Jones, An active-set approach for OFDM PAR reduction via tone reservation, IEEE Trans. Signal Process., vol. 52, no. 2, pp. 495509, Feb. 2004.



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[18] R.W. Bauml, R.F.H. Fischer and J.B. Huber, Reducing the peak-toaverage power ratio of multicarrier modulation by selected mapping, Electronics Letters, vol. 32, no. 22, pp. 2056-2057, Oct. 1996. [19] D.W.Lim, C.W. Lim, J.S. No, and H.Chung, A new SLM OFDM with low complexity for PAPR reduction, IEEE Signal proc. Lett, vol. 12, no. 2, pp. 93-96, Feb. 2005. [20] Wang and Y. Cao, Sub-optimum PTS for PAPR reduction of OFDM signals, IEEE Electronics Letters, vol. 44, no. 15, July 2008. [21] Serkan Dursun, Artyom M.Grigoryan, Nonlinear L2-by-3 transform for PAPR reduction in OFDM systems, Computers and Electrical Engineering, Elsevier, March 2010.



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